Pressure Effect on an Ocean-Based Humidification-Dehumidification Desalination Process.” Desalination 468 (October 15, 2019): 114056

University of Texas Rio Grande Valley ScholarWorks @ UTRGV

Mechanical Engineering Faculty Publications and Presentations College of Engineering and Computer Science

10-15-2019

Pressure effect on an ocean-based humidification- dehumidification desalination process

Yingchen Yang The University of Texas Rio Grande Valley, [email protected]

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Recommended Citation Yang, Yingchen. “Pressure Effect on an Ocean-Based Humidification-Dehumidification Desalination Process.” Desalination 468 (October 15, 2019): 114056. https://doi.org/10.1016/j.desal.2019.06.022.

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Pressure effect on an ocean-based humidification-dehumidification desalination process

Yingchen Yang

Department of Mechanical Engineering University of Texas Rio Grande Valley BrownsvilleEdinburgHarlingen, TX, USA

Abstract

A new humidification-dehumidification (HDH) desalination process is proposed and analyzed. Being ocean based, the process does not produce any brine. It is largely powered jointly by solar energy, wind energy, and various types of ocean energies in a nearly natural way. A vacuum pump is employed to drive the air circulation throughout the HDH process. It is the only unit that consumes electricity. The HDH process is analyzed under various conditions, including using a low pressure (as low as to 0.2 atm) for humidification and the ambient pressure for dehumidification, running the entire HDH process around a low pressure (as low as to 0.2 atm), and running it around the ambient pressure. The results from case studies show that applying different pressure levels to humidification and dehumidification would lead to a prohibitively high electric energy consumption of the vacuum pump. Being the most favorable operating condition, running the HDH process around the ambient pressure yields a freshwater production rate at the level of 4 to 11 푙/h per HDH line, depending on the pipe sizing and weather conditions. The associated minimum electric energy consumption of the vacuum pump is at the level of 0.9 to 1.6 kWh/m3-water. Keywords: HDH desalination, ocean based, pressure effect, freshwater production rate, electric energy consumption.

 Email address for correspondence: [email protected]

1. Introduction

Scarcity of freshwater has been worsening due to population growth, industrialization, contamination of available freshwater resources, and climate change [1]. From 2012 to 2017, water crises have consistently featured among the top three most impactful global risks in the World Economic Forum’s annual reports. At present, over a half of the world’s population (4 billion people) lives under conditions of severe water scarcity for at least one month a year [2]. By 2050, this population could increase to 75% [3].

In contrast to the scarcity of freshwater, seawater takes about 97% of the Earth’s water [4], making it an overly abundant and inexhaustible resource for freshwater production. And, currently over 40% of the global population lives within 100 km of the coast [5]. Obviously, low-cost and environment-friendly seawater desalination could effectively address the water stress issue to this large population in coastal regions worldwide.

To date, a large variety of desalination technologies, including conventional and emerging ones, have been proposed, investigated, or installed for freshwater production. In general, desalination technologies can be classified as membrane-based and thermal-based, according to the principle of operation [6]. Some technologies are particularly suited for large-scale desalination ( 100 m3/day, with the largest desalination plant reaching 624,000 m3/day [7]); operating them in a small capacity makes freshwater production on a unit volume basis too expensive. Other technologies are better suited for small-scale applications (< 100 m3/day, or even down to a level of 1 푙/day [8]); their freshwater production rates are largely limited by source availabilities and/or cost constraints. Large-scale desalination can effectively augment the supply of municipal water, whereas small- scale desalination mostly meets decentralized needs for rural areas (including islands) and isolated homes [9, 10].

Most commonly used conventional large-scale desalination technologies include the membrane- based reverse osmosis and thermal-based multi-stage flash [11]. Presently, reverse osmosis has the largest installed capacity worldwide [12], and is the most energy-efficient (but not necessarily the most cost-efficient) desalination technology in market [1]. Small-scale desalination technologies,

as opposed to the large-scale ones, are very diverse. With a particular focus on thermal-based desalination using a gas (mostly air) as a carrier medium, the small-scale technologies include humidification-dehumidification (HDH) desalination [9, 10], solar stills [8], and direct freshwater extraction from ambient air [13]. HDH desalination systems are fundamentally different from solar stills and conventional distillation systems, featuring the usage of gas flows to absorb water molecules from seawater or brackish water (humidification) and transport and dump them to a freshwater collector (dehumidification).

Numerous HDH desalination systems have been explored in recent years. A common way to categorize them is based on the cycle configuration, which defines three categories: open-air open- water, open-air closed-water, and closed-air open-water [9]. Most HDH desalination systems directly utilize renewable energy (mainly solar energy) for heating to lower the cost [14, 15]. They generally operate under relatively low temperature conditions (in comparison with conventional distillation) in the humidification process, with temperatures of inlet air and/or water being raised by a few degrees Celsius to a few tens of degrees Celsius from the ambient temperature but still below the water boiling point. The naturally existing dilute solar flux (at a level of 1000 W/m2), however, can only provide limited amount of power per unit area of an absorber to compensate the latent heat of water vaporization at a low level, largely limiting the freshwater production rates of the HDH systems. Among a large variety of solar HDH systems being explored so far, the most energy-efficient one is a multi-effect closed-air open-water system [16].

As one of the two key components—the humidifier and dehumidifier—in a typical HDH system, the humidifier can be configured in various ways employing different mechanisms, including packed bed towers, wetted-wall towers, spray towers, and bubble columns [9, 17]. Heat and mass transfer rates on the solid boundaries and/or air-water interfaces are the major concerns in design and optimization of the humidifier. Flow interaction with the internal structure of the humidifier has also been considered in some studies. For example, an earlier numerical study indicated that a high humidity level of the entrance air could adversely affect the humidifier performance under certain conditions, due to a local flow reversal that increases condensation [18]. Between humidification and dehumidification lines, heat recovery has been employed in nearly all HDH

systems. It should be noted though, that in certain HDH systems using humidifier outlet water to cool dehumidifier inlet air may increase production cost along with system productivity [19].

The carrier medium (e.g., air) is essential in HDH desalination. Either increased temperature or reduced pressure could largely enhance the capability of the medium to carry water molecules, which is in favor of humidification. The exact opposite is preferred in dehumidification. Therefore, both the temperature and pressure play a critical role in HDH desalination. A huge majority of HDH systems operates by heating for humidification and cooling for dehumidification with the pressure around the ambient pressure. In contrast, only a very few investigations have analyzed HDH systems at a largely varied pressure [20, 21].

HDH desalination systems can be either land-based (for desalination of seawater or brackish water) or ocean-based (for seawater desalination). Land-based systems permit easy construction, operation and maintenance. In fact, many solar-powered and land-based HDH desalination systems have demonstrated low cost and low-maintenance needs [14, 22]. For this reason, nearly all the HDH systems documented in the literature are land-based. In an attempt to directly use ocean energies (waves, ocean thermal, etc.) in HDH desalination, however, a very few ocean- based HDH systems have been proposed in invention disclosures [23-25].

In a much broader scope than HDH desalination, energy consumption and associated environmental impacts are critical issues all types of desalination technologies need to address. Presently, large-scale desalination (e.g., reverse osmosis, multi-stage flash, etc.) consumes a huge amount of energy in the form of thermal and electric energy derived from fossil fuels, creating a large carbon footprint [1, 10]. Under a typical desalination condition, e.g., for seawater at 35,000 ppm salt and with 50% of seawater converted to freshwater, the theoretical minimum energy consumption that is independent of the desalination method is 1.06 kWh/m3-water [1]. Current state-of-the-art seawater reverse osmosis desalination, being the most energy-efficient in market, consumes 2.5 – 4.0 kWh/m3-water [26]. In general, most desalination technologies include five typical stages – intake, pretreatment, pure water separation from seawater, post treatment, and brine discharge. Among these stages, intake and pretreatment together consume the second most energy next to pure water separation [26]. Therefore, enabling new desalination technologies to

eliminate the intake and pretreatment stages would greatly reduce the energy consumption and capital cost. It should be noted though, that pretreatment of feed water is needed for most desalination processes [27]. Brine is another factor worth considering. Brine is a byproduct of nearly all types of desalination processes. Direct discharge of brine to the ocean causes environmental issues [28]. Appropriate handling of brine, however, leads to added cost [29, 30].

To address the energy challenge, tremendous efforts and advancements have been made in utilizing renewable energy in desalination, either directly (without converting into electricity) or indirectly (converting into electricity first). Whenever possible, direct use is advantageous over indirect use since it can avoid employment of costly energy converters (e.g., photovoltaic panels, wind turbines, wave energy converters, etc.) and the associated waste of energy due to the limited conversion efficiencies. Direct-use renewable energy sources include solar [31, 32], geothermal [33, 34], ocean wave energy [35, 36], and ocean salinity gradient energy [37]. For HDH desalination, direct use of solar energy is very common. Direct use of ocean thermal energy (mainly for cooling in dehumidification) and ocean wave energy have also been proposed in invention disclosures [23-25]. Nonetheless, a direct and joint usage of multiple renewable energy sources to increase the freshwater production and lower the cost is yet to be demonstrated.

To address some common issues associated with the HDH desalination in general, and to gain new knowledge of pressure effect in the HDH process, an ocean-based and surface-floating HDH desalination system is proposed and discussed in the present research. The system directly uses multiple renewable energy sources to power the HDH process, with a vacuum pump to be the only unit that consumes electricity. It could work under different types of pressure conditions to achieve a desired HDH performance. The ocean deployment (by, or close to, the shoreline) enables a much simpler process with no intake and pretreatment stages and no brine production. The focus of the present work is to gain fundamental understanding by analytical means to guide the design of such an HDH system.

2. The Proposed HDH System

As schematically illustrated in Fig. 1, the proposed HDH system comprises a humidifier, a vacuum pump, a freshwater tank, pipelines, and a throttling valve. These units form a closed-air open-water system. The system essentially has two subsystems – a humidification line as indicated by dashed arrows and a dehumidification line denoted by solid arrows. The vacuum pump coordinates with the throttling valve to realize different pressure levels in the two lines. The vacuum pump also drives the air circulation throughout the entire HDH system. In the following, the working principle of the system is discussed in detail. Some key positions are numbered from 1 to 8 as shown in Fig. 1 to ease the discussion.

Figure 1: The proposed HDH desalination system.

Heating process: 1→2→3. The heating process of the dry airflow starts immediately after the throttling valve at position 1. Initially the dry air has a temperature below the ambient temperature by certain degrees Celsius (e.g., 10C below). It moves along a submerged pipe segment (1→2). This pipe segment has a high thermal conductivity, so the airflow inside is gradually heated up by the surrounding seawater by means of ocean thermal energy and reaches the ambient temperature. Waves, tides and ocean currents broadly exist in the ocean and carry ocean hydrokinetic energy. Driven by that, a huge body of the seawater continuously moves irregularly in the open ocean.

Therefore, it can naturally and effectively maintain the ambient temperature around the pipe all the time. In the next step, the temperature-recovered dry air goes into an utterly above-water pipe segment (2→3) – a solar thermal heater. The heater absorbs solar energy and raises the temperature of the inside airflow by certain degrees Celsius (e.g., 30C or more) above the ambient temperature. Note that the heater generally has a good thermal insulation capability to prevent energy loss.

Humidification process: 3→4. After the two-step heating, the warm dry air enters the humidification chamber, and grazes past wetted surfaces to gain humidity. The humidification process can be further enhanced by heating the in-chamber water by means of heat recovery (to be discussed in the following) and solar heating. The wetted surfaces are provided by a stack of partially submerged circular discs spaced out along a horizontal axle. Cloth and/or some structural patterns can be applied to the disc surfaces to increase the water carrying capability of the surfaces and enhance heat and mass transfer on the surfaces through flow interaction with the structure. The shear stress resulted on the surfaces by the grazing airflow automatically drives the stack of discs to slowly rotate about the horizontal axle and continuously bring fresh wet surfaces into contact with the airflow. Note that the humidification chamber has an open bottom, which allows free mixing of the in-chamber seawater and the surrounding seawater. Such free mixing, naturally driven by the ocean hydrokinetic energy and further enhanced by rotation of the stack of discs, maintains the salinity of the in-chamber seawater at nearly the same level with the surrounding seawater all the time. Obviously, such an HDH process has no needs for intake and pretreatment. And, it literally produces zero brine just like the natural hydrologic cycle. Also note that the water level inside the dehumidification chamber could be higher than the average ocean surface level if a vacuum pressure is created in the humidification line that includes the humidification chamber.

Settlement and pressure regulation: 4→5. Upon exiting the humidifier at position 4, the moisture- laden air enters a vertical passage to reach the vacuum pump. This vertical passage serves as a settlement chamber to allow entrained heavy impurities, if any, to fall down due to gravity and return to seawater. After the vacuum pump, the moisture-laden air is compressed to a relatively high pressure with a temperature increase due to the power input from the pump. The temperature increase can vary largely, depending on the desired pressure gain through the pump.

Cooling and dehumidification processes: 5→6→7→8→1. After position 5, the moisture-laden air moves along the dehumidification line as denoted by solid arrows in Fig. 1 and goes through three cooling phases as discussed in the following. As a result, condensation occurs with continuous heat release. The entire dehumidification line, including the tank and pipes, are made of highly thermal-conductive materials. All the pipe segments for cooling are tilted away from the horizontal direction to allow the condensed freshwater anywhere in the pipeline to eventually flow into the freshwater tank, driven by the gravity.

Cooling phase I: 5→6. As illustrated in Fig.1, a thin pipe winds through the humidification chamber right beneath the water surface. While the moisture-laden air flowing through this pipe segment is hot, the seawater in the humidification chamber is relatively cold. The heat exchange then results in initial cooling of the air and local heating of the seawater. The emphasis herein is on the seawater heating rather than the air cooling, since raising the temperature of the in-chamber seawater is much needed for humidification as addressed in the foregoing, and the hot air has more chances to be further cooled in later phases. This pipe segment is placed as close to the free surface of the in-chamber seawater as possible because the humidification chamber has an open bottom, permitting a quick mixing and exchange of the in-chamber seawater and surrounding seawater but giving the in-chamber surface seawater more time to absorb heat. Note that the presence of the pipe segment inside the humidification chamber does not interfere with rotation of the stack of discs and surface wetting. The pipes run through gaps between the circular discs only.

Cooling phase II: 6→7→8. Starting from position 6, the moisture-laden air passes through the freshwater tank and enters the next underwater pipe segment (7→8). Open ocean water moves all the time and dissipates heat quickly. Special designs can be implemented to the tank and pipe to increase the cooling surface and enhance condensation. Examples include employing a large number of pipes with small diameters, using fin structures [9] or string arrays [38], etc. At the end of this cooling phase, position 8, the temperature of the in-pipe moist air drops to the ambient temperature, and a portion of freshwater extraction is achieved.

Cooling phase III: 8→1. The moist air goes into a barely above-water pipe segment (8→1) for continuous cooling and dehumidification. This above-water pipe segment can be reached, and maintained wet on the outside, by waves. It uses evaporative cooling enhanced by winds to bring the temperature down. A shade from the above-laying solar-heating pipe segment (2→3, typically an array of pipelines) helps even more in sunny days. As a result, the temperature of the in-pipe moist air could drop by more than 10C below the ambient temperature, allowing more freshwater extraction. The dehumidification process ends right before the throttling valve at position 1, and the cold dry air is ready to go through the valve and start the next cycle of the HDH process.

Renewable energy and heat recovery. In the HDH desalination process in Fig. 1, multiple renewable energy sources are directly used in heating for humidification, cooling for dehumidification, and mixing and transporting for maintaining the salinity and temperature levels. For example, in the humidification line 1→2→3→4, the submerged pipe segment 1→2 uses ocean thermal energy assisted by ocean hydrokinetic energy for heating, the above-water segment 2→3 uses solar energy for heating, and the humidification chamber 3→4 uses solar energy for heating and ocean hydrokinetic energy for maintaining the salinity level of the in-chamber seawater. In the dehumidification line 5→6→7→8→1, the submerged tank and pipelines 5→6→7→8 use ocean thermal energy assisted by ocean hydrokinetic energy for cooling, and the above-water pipe segment 8→1 uses wave energy and wind energy for evaporative cooling. Heat recovery makes energy utilization more efficient. By means of heat recovery, the energy rejected in cooling for dehumidification is partially used in heating for humidification. This approach is reflected between the energy-rejecting pipe segment 5→6 and the energy-absorbing seawater inside the humidifier chamber, and between the two closely placed parallel pipe segments 7→8 and 1→2 in the open ocean water.

In summary, the proposed HDH desalination system in Fig. 1 has no intake or pretreatment stage and produces zero brine. The process is largely powered by multiple renewable energy sources (i.e., solar, wind, wave, tidal, ocean current, and ocean thermal) in their natural forms (direct use) and in a combined fashion. A vacuum pump is the only device in the whole system that consumes electricity. The system has a very simple overall structure. And, renewable energy sources on the

ocean site are very abundant. Jointly considering these factors, the system demonstrates a strong potential to produce freshwater at a high rate and a low cost compared to other HDH technologies.

3. Analyses Based on Psychrometry, Thermodynamics, and Fluid Mechanics

In support of the HDH desalination approach discussed in the foregoing and to guide the engineering design of such an HDH system, some basic analyses have been performed. They are based on psychrometry, thermodynamics, and fluid mechanics.

3.1. Water Carrying Capability of Air

An online humidity calculator [39] was used to obtain some data, which reveal the water carrying capability of air in relation to the temperature and pressure. The HDH process employs dry air as a medium to absorb water vapor and form moist air. The amount of water vapor that air may contain at a specified temperature and pressure reaches the maximum at saturation, and the corresponding relative humidity (RH) is 100%. Fig. 2 shows the mixing ratio (x) of moist air, defined as the ratio of mass of water vapor (푚푣, kg-water) to mass of dry air (푚푎, kg-air), as a function of pressure (p) at a few fixed values of temperature (T) and at 100% RH. Focusing on individual curves, the mixing ratio increases with reduced pressure at a fixed temperature. The closer of the pressure approaches the water boiling point (towards the left of each curve), the faster the mixing ratio grows. Comparing the three representative curves, the mixing ratio goes up with increased temperature at a fixed pressure (e.g., p = 0.2 atm).

Figure 2: Variation of mixing ratio 푥 with pressure 푝 at three specified values of temperature 푇.

3.2. A Thermodynamic Model for Temperature and Energy Analyses

In the examined ranges of pressure and temperature in the present study, the moist air as well as its constituent air and vapor components all obey the ideal gas law with sufficient accuracy, and the thermodynamic properties of the moist air can be obtained by means of linear superposition of the corresponding air and vapor properties [40, 41]. The ideal gas properties (e.g., specific enthalpy h and entropy function so) of dry air and water vapor are available in Tables A-22 and A-23 of reference [42]. Eqs. 1 – 6 provides an approach to determine needed properties of the moist air, which are of particular interest in the present study. In Eqs. 1 – 6, symbols with subscripts a and v denotes corresponding properties of air and water vapor, respectively (e.g., partial pressures 푝푎 표 표 and 푝푣, entropy functions 푠푎 and 푠푣 , specific entropies 푠푎 and 푠푣, enthalpies ℎ푎 and ℎ푣, and gas constants 푅푎 and 푅푣). Symbols with no subscripts represents corresponding properties of the moist air as a mixture (e.g., total pressure p, specific entropy s, and specific enthalpy h). To calculate h and s of the moist air at given T, p and RH, the mixing ratio x needs to be determined first [39], followed by 푝푣 and 푝푎 using Eqs. 1 & 2 [40], 푠푎 and 푠푣 using Eqs. 3 & 4 [42], and then h and s using Eqs. 5 & 6 [40]. Note that the specific enthalpy h and specific entropy s of the moist air are based on unit mass of dry air.

푝푣 = 푥푝/(0.622 + 푥) (1)

푝푎 = 푝 − 푝푣 (2)

표 푝푎 푠푎 = 푠푎 − 푅푎푙푛 (3) 푝푟푒푓,푎

표 푝푣 푠푣 = 푠푣 − 푅푣푙푛 (4) 푝푟푒푓,푣

ℎ = ℎ푎 + 푥ℎ푣 (5)

푠 = 푠푎 + 푥푠푣 (6)

Upon the availability of these thermodynamic properties, the proposed HDH desalination system of Fig. 1 can be analyzed from thermodynamics perspective. Particularly, the temperature gain of the circulating moist air through solar thermal heating, the temperature drop of it due to humidity gain in humidification, and the minimum electric energy consumption of the vacuum pump per unit volume of freshwater production can be quantified. For easy discussion, the position numbers

in the HDH system of Fig. 1 are used as subscripts to denote properties/parameters of the moist airflow at the corresponding positions. For example, position 3 indicates the inlet of the humidifier. At this position, the temperature (푇), pressure (푝), mixing ratio (푥), specific enthalpy (ℎ), specific entropy (푠), and the average airflow velocity (푉) are denoted as 푇3 , 푝3 , 푥3 , ℎ3 , 푠3 , and 푉3 accordingly.

Solar thermal heating 2→3 in Fig. 1 leads to a temperature gain 푇3 − 푇2. By selecting the pipe segment 2→3 as a control volume and apply the first law of thermodynamics, it gives 푄̇ ℎ3 = ℎ2 + , (7) 푚̇ 1 where 푚̇ 1 is the mass flow rate of the moist air at position 1 (푚̇ 1 = 푚̇ 2 = 푚̇ 3), and 푄̇ is the heat transfer rate due to the solar irradiance. 푄̇ is obtained by conservatively assuming a 50% conversion efficiency of the 1-kW/m2 solar power intensity, which is in comparison with 70-90% efficiencies of industrial solar thermal heaters and accounts for humidity effect over the ocean surface. For moist air as an ideal gas at a specified 푥, ℎ is a function of 푇 only (implicitly by means of Eq. 5 and the thermodynamic property tables [42]). In this heating phase there is no humidity gain or loss, 푥2 = 푥3 . Therefore, a given 푇2 is associated with a known ℎ2 , which leads to determination of ℎ3 using Eq. 7. Inversely, the resulted ℎ3 defines 푇3.

In the humidification process 3→4, the grazing airflow loses energy to the surface water (mainly on the roller discs), leading to a temperature drop (푇4 < 푇3) of the airflow and a humidity gain

(푥4 > 푥3) through evaporation. Select the humidifier as a control volume, and assume a 100% energy transfer from the entering airflow at 푇3 to the surface water that evaporates at 푇4. Other means of energy gain (e.g., solar thermal heating on the humidifier) or loss are neglected. Note that 푇4 should be still above the ambient temperature. Heat recovery as discussed in Section 2 can help bring the surface water temperature from the ambient temperature to 푇4 through careful design. Applying the first law of thermodynamics to the control volume (excluding the heat recovery part but assuming the surface water at 푇4) gives

(1 + 푥4)ℎ4 = (1 + 푥3)ℎ3 + (푥4 − 푥3)ℎ푤, (8) where ℎ푤 is the specific enthalpy of liquid water at 푇4. In this equation, 푥4, ℎ푤 and ℎ4 all depend on 푇4. The equation can be solved through iteration by using thermodynamic property tables [42]

in conjunction with the online humidity calculator [39]. Then with known ℎ4, 푇4 can be found from the property tables.

The vacuum pump 4→5 in the HDH desalination system of Fig. 1 is the only unit that consumes electricity. Other than that, the entire HDH process is directly powered by multiple renewable energy sources in a nearly natural way with very low cost. Choose the vacuum pump in steady- state operation as a control volume. Assume that after a perfect humidification, the moist air reaches a desired humidity level of 100% RH at position 4 with 푇4, 푝4 and 푥4. The moist air then goes through the vacuum pump and the outlet pressure at position 5 rises to a desired level 푝5. In this thermodynamic process, no condensation occurs; the pressure increase through the vacuum pump is accompanied by a temperature increase due to the power input. Therefore, the mixing ratio remains unchanged from the inlet to the outlet, 푥4 = 푥5. Now with known 푇4, 푝4 and 푝5, the minimum power input can be achieved by assuming an isentropic process, 푠4 = 푠5. Then based on the first law of thermodynamics, the minimum electric power input (푊̇ ) per mass flow rate of dry air (푚̇ 푎) is equal to the enthalpy increase,

푊̇ /푚̇ 푎 = ℎ5 − ℎ4. (9)

In this equation, ℎ4 can be determined using 푇4, 푝4 and 푥4, whereas ℎ5 depends on 푝5, 푠5 (= 푠4) and 푥5 (= 푥4).

After the vacuum pump the moist air goes through a series of cooling phases for dehumidification until it reaches the inlet of the throttling valve at position 1. The mixing ratio 푥1 at this position can be determined with given 푇1, 푝1 and 100% RH using the same online humidity calculator as mentioned before. Then based on Eq. 9, the minimum electric energy consumption per unit volume of freshwater production in liquid phase can be determined as

998(ℎ5 − ℎ4) 푊푤 = , (10) 3600(푥4 − 푥1) 3 where ℎ4 and ℎ5 are in kJ/kg, and 푊푤 is in kWh/m -water. Additionally, with known 푥1, 푥4 and

푚̇ 1, the freshwater production rate 푚̇ 푤 can be calculated using

3600(푥4 − 푥1)푚̇ 1 푚̇ 푤 = , (11) 0.998(1 + 푥1) where 푚̇ 1 is in kg/s, and 푚̇ 푤 is in 푙/h of liquid water.

3.3. A Fluid Mechanics Model for Pressure Loss Estimate

As evident in Fig. 2, a low pressure is in favor of humidification and a high pressure in dehumidification. To keep air circulation in the HDH process as illustrated in Fig. 1, a minimum pressure gain from the inlet 4 to the outlet 5 of the vacuum pump is needed. This gain is used to overcome the pressure loss in the humidification and dehumidification lines as well as on the rolling discs of the humidifier. If the humidification line and dehumidification line need to be set at different pressure levels, the pump’s pressure gain should be greater than the minimum one; the additional pressure gain is to be applied on the throttling valve to achieve the expected pressure levels.

To quantify the pressure loss in the humidification and dehumidification lines in Fig. 1, the viscosity 휇 (in Pas) and density 휌 (in kg/m3) of the humid air at a specified temperature 푇 (in K), pressure 푝 (in Pa), and mixing ratio 푥 can be determined using [43]: 휇 휇 휇 = 푎 + 푣 , (12) 휇 0.5 2 휇 0.5 2 1 + 0.3519 [1 + 0.8881 ( 푎) ] ∙ 푥 1 + 0.1727 [1 + 1.1260 ( 푣) ] /푥 휇푣 휇푎 6 −5 2 −8 3 −12 4 휇푎 ∙ 10 = 0.40401 + 0.074582푇 − 5.7171 ∙ 10 푇 + 2.9928 ∙ 10 푇 − 6.2524 ∙ 10 푇 , (13)

√ 푇 6 647.27 휇푣 ∙ 10 = , (14) 647.27 647.27 2 647.27 3 0.0181583 + 0.0177624 ( ) + 0.0105287 ( ) − 0.0036744 ( ) 푇 푇 푇 1 + 푥 푝 휌 = ∙ . (15) 461.56 ∙ (0.62198 + 푥) 푇

Upon determination of 휇 and 휌, the pressure loss Δ푝 of a fully developed turbulent internal flow of moist air along a circular pipe at a constant temperature 푇 with no occurrence of condensation can be calculated using the following equations [44]: 휌푉퐷 푅푒 = , (16) 휇 1 6.9 휀/퐷 1.11 ≈ −1.8푙표푔 [ + ( ) ], (17) 푓1/2 푅푒 3.7

푓퐿휌푉2 Δ푝 = . (18) 2퐷 In these equations, 푅푒 is the Reynolds number, 푉 the average flow velocity of moist air, 퐷 the pipe inner diameter, 휀 the pipe inner surface roughness, 퐿 the pipe length, and 푓 the Darcy friction factor. Eq. 17 applies to turbulent pipe flow, which occurs when 푅푒 ≥ 4000 [44].

The pipe flow in the proposed HDH system in Fig. 1 has varied temperature 푇 and mixing ratio 푥, which complicate the pressure loss calculation. Focusing on the airflow along the pipeline between the freshwater tank (position 7) and the throttling valve (position 1), the moist air undergoes two cooling phases – ocean thermal cooling 7→8 and evaporative cooling 8→1. Condensation occurs in these two phases at 100% RH, and the mixing ratio decreases with decreasing temperature. In contrast, the airflow along the pipeline between the throttling valve (position 1) and the humidifier (position 3) experiences two heating phases – ocean thermal heating 1→2, and solar thermal heating 2→3. The air in these heating phases has no gain or loss of water. Hence, the relative humidity decreases with increasing temperature, but the mixing ratio remains constant.

To apply Eqs. 12 – 18 for an approximate estimate of a total pressure loss along a pipe length 퐿, and to deal with the variations in temperature, mixing ratio and other parameters, the full pipe length 퐿 is divided into a large number of differential length 푑퐿 for differential pressure 푑푝 first. Then the total pressure loss is obtained through numerical integration. In doing so, the temperature distribution along the pipe needs to be known. Additionally, the local velocity 푉 at any position along the pipe can be determined using

1 + 푥 휌1 푉 = 푉1. (19) 1 + 푥1 휌 This equation is derived from mass conservation. In applying Eqs. 12 – 19 to determine the total pressure loss, the pressure drop due to the presence of the throttling valve is excluded. Minor losses on the pipe fittings (e.g., elbows/bents, etc.) are also ignored.

4. Case Studies

Consider an HDH system as illustrated in Fig. 1 in a utility scale. A pipe of inner diameter 퐷 = 0.15 m and length 퐿 = 100 m is employed along the airflow direction 7→8→1→2→3. In practice, arrays of such pipes are to be applied in parallel to gain a high production rate of freshwater. Assume that the full length 퐿 is evenly divided into four segments: 7→8 for ocean thermal cooling, 8→1 for evaporative cooling, 1→2 for ocean thermal heating, and 2→3 for solar thermal heating. In this case study, two scenarios are analyzed – without throttling and with throttling.

4.1. An HDH System without Throttling

In this scenario, the throttling valve at position 1 is removed from the HDH system in Fig. 1. Some temperature conditions are given, assumed (based on some educated guesses, or for the easiness of analysis), and/or derived. They are discussed as follows. (1) At positions 2 and 8, the temperature recovers to a specified ambient temperature (e.g., 푇2 = 푇8 = 10C, 20C, 30C, or

40C). (2) A 10C temperature drop is assumed through evaporative cooling (8→1), 푇1 = 푇8 −

10C; the real temperature drop could be largely affected by the wind condition. (3) 푇3 at the end of solar thermal heating (2→3) is obtained using Eq. 7 implicitly. (4) 푇4 at the end of the humidification process (3→4) is determined using Eq. 8 implicitly. (5) 푇5 at the outlet of the vacuum pump is found with known 푇4, 푝4 & 푝5 and by assuming an isentropic process through the vacuum pump (for the minimum electric power consumption). (6) 푇7 is set by assuming 푇5 −

푇7 = (푇5 − 푇8)/3. (7) Linear temperature distributions are assumed in the pipe segments 7→8, 8→1, 1→2, and 2→3.

In addition to the temperature information, the pressure 푝1 and the average velocity 푉1 are also set to be the controlling parameters in this case study. The pressures 푝2, 푝3, 푝7, and 푝8 then become determinable using Eqs. 12 – 19 together with the online humidity calculator [39]. The pressures

푝4 and 푝5 can be largely affected by the detailed humidification and heat recovery mechanisms.

Their levels are roughly set by assuming 푝3 − 푝4 ≈ 푝1 − 푝3 and 푝5 − 푝7 ≈ 푝7 − 푝1, based on an educated guess. This assumption leads to ∆푝푣푎푐푢푢푚 = 2∆푝7−3, where ∆푝푣푎푐푢푢푚 is the pressure gain through the vacuum pump, ∆푝푣푎푐푢푢푚 = 푝5 − 푝4, and ∆푝7−3 = 푝7 − 푝3. Then with known

푝4, 푝5 and other information as needed, the minimum electric energy consumption of the vacuum pump can be quantified using Eq. 10.

Using the above conditions and approaches, the first computation run was conducted at 푇1 = 10C,

푝1 = 1 atm, and 푉1 = 2.5 m/s. The results of some parameters at the positions numbered in Fig. 1 are summarized in Table 1. Additionally, the pressure drop between positions 7 and 3 is ∆푝7−3 = -4 6.56×10 atm, the freshwater production rate is 푚̇ 푤 = 5.24 푙/h, and the vacuum pump’s minimum 3 electric energy consumption is 푊푤 = 1.26 kWh/m -water. The computation conditions and results are further interpreted as follows.

Table 1: Computation results at 푝1 = 1 atm, 푇1 = 10C, and 푉1 = 2.5 m/s. 푝 푇 푉 ℎ 푠 Position (atm) (C) 푥 (m/s) 푅푒 (kJ/kg) (kJ/kg·K) 1 1.00000 10.0 0.0076 2.50 26626 287.3 1.74 2 0.99984 20.0 0.0076 2.58 25911 297.4 1.78 3 0.99967 53.6 0.0076 2.88 23856 331.7 1.89 4 0.99934 33.9 0.0344 × × 326.8 2.15 5 1.00066 34.0 0.0344 × × 326.9 2.15 7 1.00033 29.4 0.0262 2.75 26107 317.4 2.04 8 1.00016 20.0 0.0147 2.62 26233 301.3 1.86

The temperature 푇1 = 10C is associated with an ambient temperature of 20C (푇2 and 푇8). The -4 pressure 푝1 = 1 atm and the pressure drop ∆푝7−3 = 6.56×10 atm jointly define the pressure level throughout the HDH system to be at the ambient pressure with very little changes. The velocity

푉1 = 2.5 m/s is equivalent to a light breeze according to the Beaufort wind scale, which is low enough to permit easy occurrence of condensation. The Reynolds number 푅푒1 = 26626 ensures a fully turbulent pipe flow (푅푒 > 4000) that is in favor of quick heat exchanging between the in- pipe moist air and the surrounding environment. The freshwater production rate per HDH line,

푚̇ 푤 = 5.24 푙/h, is very promising compared to other state-of-the-art HDH desalination processes 3 [10]. Most importantly, the minimum electric energy consumption 푊푤 = 1.26 kWh/m -water is

very close to the theoretical minimum energy consumption of 1.06 kWh/m3-water [1], and is much lower than the state-of-the-art level of 2.5 – 4.0 kWh/m3-water [26]. Of course, such a low energy consumption level of the present approach is achieved by counting the pump’s minimum electric energy consumption only, assuming that the rest of the system is directly and sufficiently powered by all kinds of renewable energy sources at a very low cost as discussed in the forgoing.

To further reflect an overall HDH cycle (1→2→3→4→5→7→8→1) of the moist air in this first computation run, a 푇 − 푠 diagram is presented in Fig. 3. A linear connection between any two adjacent data points is made as an approximation, just for the illustration purpose.

Figure 3: T – s diagram of an HDH cycle at 푝1 = 1 atm, 푇1 = 10C, and 푉1 = 2.5 m/s.

Based on the first computation run discussed in the foregoing, more runs were conducted at a fixed

-4 temperature 푇1 = 10C, a fixed pressure drop ∆푝7−3 = 6.56×10 atm, and a varied pressure 푝1 in the range of 0.2 – 1 atm (in vacuum conditions). Unlike the first run where 푉1 is given and ∆푝7−3 is derived, now 푉1 becomes derived and ∆푝7−3 is given. The computation results are summarized in Table 2. They are also graphically presented in Fig. 4; each plot reflects a trend of a parameter with varied 푝1. Note that the pressure gain created by the vacuum pump, ∆푝푣푎푐푢푢푚, is twice the −3 pressure drop ∆푝7−3 (as assumed earlier): ∆푝푣푎푐푢푢푚 = 2∆푝7−3 = 1.31 × 10 atm. Therefore, the data in Table 2 and Fig. 4 reflect the system performance at a fixed pressure gain of the vacuum pump. Also note that this pressure gain is about two to three orders lower than the values of 푝1 examined. Hence 푝1 very closely represents the actual pressure level everywhere in the system.

-4 Table 2: Computation results at 푇1 = 10C and ∆푝7−3 = 6.56×10 atm under varied 푝1.

푝1 푇3 푇4 푇5 푚̇ 1 푚̇ 푤 푊푤 푅푒 3 (atm) (C) (C) (C) 1 (kg/s) (푙/h) (kWh/m ) 1.0 53.6 33.9 34.0 26626 0.0548 5.24 1.26 0.8 58.1 33.6 33.8 23427 0.0482 5.71 1.30 0.6 64.8 32.9 33.1 19845 0.0407 6.24 1.33 0.4 76.2 31.4 31.7 15684 0.0320 6.83 1.49 0.2 102.6 27.7 28.3 10445 0.0210 7.31 1.94

It is evident in Fig. 4 that, the lower the pressure 푝1, the higher the freshwater production rate 푚̇ 푤

(Fig. 4b). Especially, this increased 푚̇ 푤 (with lowered 푝1) is achieved on a decreased mass flow rate 푚̇ 1 of the moist air (Fig. 4c). It is noteworthy though, that the increase of 푚̇ 푤 is very limited in comparison with the significant decrease of 푝1. It is more disappointing that, the lowered pressure 푝1 results in an increased minimum electric energy consumption 푊푤 (Fig. 4a). The lower the pressure 푝1 becomes, the faster 푊푤 grows. Therefore, it is economically disadvantageous to achieve an increased freshwater production rate by operating the HDH system around a vacuum pressure rather than around the ambient pressure, not to mention the complexity and additional cost on maintaining such a vacuum pressure in routine operation.

In the examined range of 푝1 in Fig. 4, the Reynolds number 푅푒1 indicates a turbulent pipe flow condition in all the computation runs (Fig. 4d). At lowered 푝1, solar thermal heating leads to climbed 푇3 (Fig. 4e) due to reduced 푚̇ 1 (Fig. 4c). After humidification, however, 푇4 shows a declined trend with lowered 푝1 (Fig. 4f). This trend is mainly resulted by an enhanced evaporation of the liquid water due to the reduced pressure.

(f)

(e)

(d)

(c)

(b)

(a)

Figure 4: Graphical presentation of the results in Table 2. (a) 푊푤 versus 푝1. (b) 푚̇ 푤 versus 푝1. (c) 푚̇ 1 versus 푝1. (d) 푅푒1 versus 푝1. (e) 푇3 versus 푝1. (f) 푇4 & 푇5 versus 푝1.

With a preferred operation condition given to 푝1 = 1 atm, and by maintaining the same pressure -4 drop ∆푝7−3 = 6.56×10 atm as before, further computation runs were conducted at varied 푇1 in the range of 0 – 30C. The results are provided in Table 3. Among the parameters listed in Table

3, 푊푤 and 푚̇ 푤 are plotted against 푇2 in Fig. 5. Note that 푇2 (= 푇1 + 10C) also represents the

ambient temperature. Therefore, Table 3 and Fig. 5 show the effect of the ambient temperature on the system performance.

-4 Table 3: Computation results at 푝1 = 1 atm and ∆푝7−3 = 6.56×10 atm under varied 푇1.

푇1 푇2 푇3 푇4 푇5 푚̇ 1 푚̇ 푤 푊푤 푅푒 3 (C) (C) (C) (C) (C) 1 (kg/s) (푙/h) (kWh/m ) 30 40 74.1 45.6 45.7 24281 0.0520 7.33 0.94 20 30 64.0 39.7 39.9 25384 0.0534 6.36 1.07 10 20 53.6 33.9 34.0 26626 0.0548 5.24 1.26 0 10 43.0 27.9 28.0 28014 0.0562 4.09 1.62

In the examined range of the ambient temperature 10C ≤ 푇2 ≤ 40C, the lower and upper ends represent ocean surface conditions on a chilly day and a hot day, respectively. As show in Table 3 and Fig. 5, with increase of the ambient temperature from 10C to 40C, the freshwater production rate 푚̇ 푤 increased from 4.09 to 7.33 푙 /h, and the vacuum pump’s minimum electric energy 3 consumption 푊푤 reduced from 1.62 to 0.94 kWh/m -water. Undoubtedly, a hot weather is in favor of the HDH desalination over a chilly weather. Still, in the entire temperature range being examined, both 푚̇ 푤 and 푊푤 demonstrate a very promising system performance.

(b)

(a)

Figure 5: Graphical presentation of partial results in Table 3. (a) 푊푤 versus 푇2. (b) 푚̇ 푤 versus 푇2.

From a practical point of view, arrays of HDH lines instead of just a single one as illustrated in Fig. 1 can be employed in building a desalination plant for a high freshwater production rate. The single line freshwater production rate can also be greatly enhanced through parametric optimization. For example, by doubling the pipe diameter 퐷 from 0.15 m to 0.3 m and maintaining the average air velocity 푉1 = 2.5 m/s and all the other conditions the same as before, at a comfortable ambient temperature 푇2 = 20C and an in-pipe pressure 푝1 = 1 atm, a single line HDH system can produce freshwater at a rate of 푚̇ 푤 = 11.12 푙/h with the minimum electric energy 3 consumption of the vacuum pump to be 푊푤 = 0.96 kWh/m -water. The results are in comparison 3 with 푚̇ 푤 = 5.24 푙/h and 푊푤 = 1.26 kWh/m -water at 퐷 = 0.15 m. Of course, such results are based on an assumption that the renewable energy sources are sufficient enough to provide appropriate heating and cooling as needed.

4.2. An HDH System with Throttling

Focus on the pipe diameter 퐷 = 0.15 m as before. In this new scenario, the throttling valve in Fig.

1 is employed to generate a preset pressure drop ∆푝푡ℎ푟표푡푡푙푒 between its inlet (namely position 1) and outlet (namely position 1). Such a pressure drop will separate the pressure levels between the humidification line 1→2→3→4 and the dehumidification line 5→6→7→8→1, hoping to achieve a better system performance than without throttling.

For ideal gas going through a throttling process, there is no temperature change [42]. Since the moist air is assumed to be ideal gas in the present study, the temperature throughout the throttling valve would remain the same and is denoted as 푇1 as before. The other temperature conditions in this scenario are exactly the same as that in the earlier scenario. On the pressure in this scenario,

푝1 and 푝1′ are for the inlet (position 1) and outlet (position 1) pressure levels of the throttling valve, 푝1 − 푝1′ = ∆푝푡ℎ푟표푡푡푙푒. Other pressure conditions are the same as before and are summarize herein: 푝3 − 푝4 ≈ 푝1′ − 푝3 , 푝5 − 푝7 ≈ 푝7 − 푝1 . Based on these pressure specifications, the vacuum pump needs to create a pressure gain ∆푝푣푎푐푢푢푚 = 푝5 − 푝4 = 2(푝7 − 푝1) + ∆푝푡ℎ푟표푡푡푙푒 +

2(푝1′ − 푝3), where 푝7 − 푝1 and 푝1′ − 푝3 are computed and ∆푝푡ℎ푟표푡푡푙푒 is preset.

-4 By maintaining (푝7 − 푝1) + (푝1′ − 푝3) = 6.56×10 atm as before, the system performance at fixed 푝1 = 1 atm and 푇1 = 10C and varied ∆푝푡ℎ푟표푡푡푙푒 is presented in Fig. 6. It is evident that, with increase of ∆푝푡ℎ푟표푡푡푙푒 from 0 to 0.1 atm, the freshwater production rate 푚̇ 푤 increases by very little (Fig. 5b). In contrast, the pump’s minimum electric energy consumption 푊푤 increases almost linearly (Fig. 5a).

(b)

(a)

Figure 6: Computation results at fixed 푇1 = 10C, 푝1 = 1 atm, (푝7 − 푝1) + (푝1′ − 푝3) = -4 6.56×10 atm and varied ∆푝푡ℎ푟표푡푡푙푒. (a) 푊푤 versus ∆푝푡ℎ푟표푡푡푙푒. (b) 푚̇ 푤 versus ∆푝푡ℎ푟표푡푡푙푒.

In a much larger range 0.1 < ∆푝푡ℎ푟표푡푡푙푒 < 1 atm, the pressure drop (푝7 − 푝1) + (푝1′ − 푝3) = -4 6.56×10 atm becomes negligibly small, resulting in ∆푝푡ℎ푟표푡푡푙푒 ≈ ∆푝푣푎푐푢푢푚 . Then with a particular focus on the vacuum pump alone, the pump’s minimum electric energy consumption

푊푤 can be simply determined using Eq. 10 with a given 푇4 at the inlet, 푝5 at the outlet, and the pressure gain ∆푝푣푎푐푢푢푚. Note that at the pump’s inlet the pressure 푝4 can be determined using

푝4 = 푝5 − ∆푝푣푎푐푢푢푚 . Fig. 7 shows the variation of 푊푤 with ∆푝푣푎푐푢푢푚 in the range 0 <

∆푝푣푎푐푢푢푚 < 1 atm at a fixed 푝5 = 1 atm and three specified values of 푇4. The three temperature values 푇4 = 28C, 34C and 40C are associated with 푇2 = 10C, 20C and 30C in the earlier scenario without throttling. As evident in Fig. 7, there is a peak of 푊푤 versus ∆푝푣푎푐푢푢푚 for each specified 푇4. The peaks occur in a narrow range 0.63 < ∆푝푣푎푐푢푢푚 < 0.67. For a further increased

∆푝푣푎푐푢푢푚 beyond the peak points (leading to a further reduced 푝4 = 1 − ∆푝푣푎푐푢푢푚), 푊푤 goes down until a boiling pressure of 푝4 is reached. Taking a global view of Fig. 7, however, it is obvious that 푊푤 is generally one to two orders higher than that of the state-of-the-art technologies 3 (i.e., 2.5 – 4.0 kWh/m -water [26]) in nearly the entire range 0 < ∆푝푣푎푐푢푢푚 < 1 atm except when -3 ∆푝푣푎푐푢푢푚 becomes very low (e.g. ∆푝푣푎푐푢푢푚 = 2(푝7 − 푝1) + 2(푝1′ − 푝3) = 1.31×10 atm).

Figure 7: Variation of the vacuum pump’s minimum electric energy consumption 푊푤 with its pressure gain ∆푝푣푎푐푢푢푚 at a fixed outlet pressure 푝5 = 1 atm and three specified inlet temperature 푇4 = 28C, 34C and 40C.

Taken Fig. 6a and Fig. 7 together and noting the relation ∆푝푣푎푐푢푢푚 ≈ ∆푝푡ℎ푟표푡푡푙푒, it becomes very clear that applying a throttling valve to separate the pressure levels between the humidification line 1→2→3→4 and the dehumidification line 5→6→7→8→1 of Fig. 1 is economically prohibitive. Therefore, in a practical design of the HDH system in Fig. 1, the throttling valve should be removed.

5. Conclusions

An ocean based HDH desalination process is proposed. It enables a closed-air open-water system that does not produce any brine. The process is largely powered by various renewable energy sources in a nearly natural way, with a vacuum pump to be the only unit that consumes electricity. The vacuum pump is used to drive the air circulation in the HDH process. Analytical models based on psychrometry, thermodynamics, and fluid mechanics have been developed to characterize the HDH system performance. The following conclusions are drawn from case studies:

(1) Employing a throttling valve to create a vacuum pressure level in the humidification line and maintain an ambient pressure level in the dehumidification line is disadvantageous to the HDH desalination. The pump’s minimum electric energy consumption per unit volume of freshwater production could be one to two orders higher than the total energy consumption per unit volume of freshwater production of the state-of-the-art desalination technologies.

(2) Making the air circulating through both the humidification and dehumidification lines at nearly the same vacuum pressure level without throttling leads to an increased freshwater production rate in comparison with running the air around the ambient pressure level. But the increase is very limited (about 40% increase by dropping the line pressure from 1 atm to 0.2 atm), and is based on an increase of the pump’s minimum electric energy consumption per unit volume of the freshwater production (about 55% increase).

(3) Running the circulating air through the entire HDH system around the ambient pressure without throttling (but with some pressure loss) is the most practical and economically viable way of using the proposed HDH process for seawater desalination. The yielded freshwater production rate could be at the level of 4 to 11 푙/h per HDH line, depending on the pipe sizing and weather conditions. The associated minimum electric energy consumption of the vacuum pump is at the level of 0.9 to 1.6 kWh/m3-water.

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